pregnant feral cat in Phoenix summer heat

A pregnant feral cat has adopted my lush Phoenix backyard. She pants and
looks so hot despite the shade and available water and food for her.
(Afterall, it has been over 110 degrees this past week.) I have not been able
to trap her---she seems trap-wise. I worry about where she will have the
kittens and wonder if I should build her some kind of box to protect the
family from rain and monsoon wind---to say nothing about my pitbull who hates
cats. I have been able to keep the dog away from the mother cat, because she
is wary, anyway., and the dog listens to my warnings most of the time. I
worry about kittens, however, who won't have as much experience or sense.

I had a side area that was shady and fenced off, but my neighbor cut off huge
branches of my tree which shaded this area completely. (Another story) Now,
the cat does not want to be over there, because of the sun and resulting heat.
That area WAS the good solution to this problem, but now that is gone.

OK folks, I am open to all suggestions from people who have experience with
feral cats. I have had lots of animals in my care and have never had an
unwanted litter, so I don't know what to expect from a feral labor, nest
choices, kitten behavior, possible kitten socialization & mother tolerance of
this, and whatever else I don't know to ask. I know about farm cats, but
Wisconsin farms offer mother cats lots of choices that don't exist in a hot
Phoenix neighborhood.

I will be driving to one of those Wisconsin farms in the fall, so I would be
able to find farm homes for this cat family if they are FIV and feline
leukemia free. I hope I can be accepted by the kittens so that I can get
them tested. Maybe I can use the kittens to trap the mother. Any experience
with that? HELP.